Rewrite 9x2 + 3xy + 15x + 5y in factored form. (3x + 3)(5x + y) (3x + 5)(3x + y) (3x + 5y)(3x + 1) (3x + y)(5x + 3)

To factor the expression $9x^2 + 3xy + 15x + 5y$, let's break it down step by step.

1. Break Down the Problem

We need to factor the expression $9x^2 + 3xy + 15x + 5y$ into a product of binomials.

2. Relevant Concepts

The expression can be grouped, and we can use factoring techniques, such as grouping or looking for common factors, to simplify it.

3. Analysis and Detail

Let's group the terms:

$(9x^2 + 15x) + (3xy + 5y)$

Now, factor out the common factors from each group:

1. From $9x^2 + 15x$, we can factor out $3x$: $3x(3x + 5)$

2. From $3xy + 5y$, we can factor out $y$: $y(3x + 5)$

Now, we have:

$3x(3x + 5) + y(3x + 5)$

Next, we see that $(3x + 5)$ is a common factor:

$(3x + 5)(3x + y)$

4. Verify and Summarize

To verify, we can expand $(3x + 5)(3x + y)$:

$3x \cdot 3x + 3x \cdot y + 5 \cdot 3x + 5 \cdot y = 9x^2 + 3xy + 15x + 5y$

The expansion checks out, confirming the factorization is correct.

Final Answer

The factored form of the expression $9x^2 + 3xy + 15x + 5y$ is:

$(3x + 5)(3x + y)$